This paper is devoted to a natural generalization of the problem on the chromatic number of the plane. The chromatic number of the spaces ℝn × [0, ε]k is considered. It is proved that 5 ≤ χ(ℝ2 × [0, ε]) ≤ 7 and 6 ≤ χ(ℝ2 × [0, ε]2) ≤ 7 for ε > 0 sufficiently small. Also, some natural questions arising from these considerations are posed.
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© 2018 American Mathematical Society.
- Chromatic number of Euclidean spaces
- Chromatic number of the plane